Pattern recognition, regression estimates, density estimation are a few examples of a class of problems that are analyzed using kernel-based methods. The latter are illustratively described herein in the context of pattern recognition. However, it should be noted that the inventive concept (described below) is not limited to pattern recognition and is applicable to kernel-based methods in general (of which support-vector-machines are an example).
In pattern recognition, it is known in the art to use a recognizer having a support-vector-machine (SVM) architecture. The SVM is viewed as mapping an input image onto a decision plane. The output of the SVM is typically a numerical result, the value of which is associated with whether, or not, the input image has been recognized as a particular type of image.
As a very general example, consider a 16 pixel by 16 pixel image of a tree. In this context, an SVM recognition system is first "trained" with a set of known images of a tree. For example, the SVM system could be trained on 1000 different tree images, each image represented by 256 pixels. Subsequently, during operation, or testing, the SVM system classifies input images using the training data generated from the 1000 known tree images. The SVM system indicates classification of an input image as the desired tree if, e.g., the output, or result, of the SVM is a positive number.
Unfortunately, in the above example, the recognizer may have to deal not only with a particular type of tree image, but also with translates of that tree image. For example, a tree image that is shifted in the vertical direction--but is still the same tree. To some extent this kind of translation can be dealt with by using tree images that represent such a vertical shift. However, the SVM system is still trained to predefined images, it's just that some of these predefined images are used to represent translations of the image (as opposed to, e.g., different types of trees).